A tension roller of the above-described type is shown in FIG. 2 of DE-GM 80 13 203. This tension roller has two side parts, each of which is cup-shaped and has an annular seat which extends only partly into the bearing bore. The seats extend to become radial contact surfaces which respectively abut the side surfaces of the inner ring of the bearing. The mounting of the bearing is achieved in part by radial force-fitting and in part by means of the contact surfaces which apply pressure as a result of tightening of the mounting bolt. In order that this embodiment can be used under high radial loading, the side parts must be made of relatively strong sheet metal, whereby the bearing can be force-fit only with great effort. In the case of extreme loads, the side parts must be nearly solid in construction, so that their density must be high.